A Decline Curve Analysis Model Based on Fluid Flow Mechanisms

Abstract

Abstract Decline curve analysis models are frequently used but still have many limitations. Approaches of decline curve analysis used for naturally-fractured reservoirs developed by water flooding have been few. To this end, a decline analysis model derived based on fluid flow mechanisms was proposed and used to analyze the oil production data from naturally-fractured reservoirs developed by water flooding. Relative permeability and capillary pressure were included in this model. The model reveals a linear relationship between the oil production rate and the reciprocal of the oil recovery or the accumulated oil production. We applied the model to the oil production data from different types of reservoirs and found a linear relationship between the production rate and the reciprocal of the oil recovery as foreseen by the model, especially at the late period of production. The values of the maximum oil recovery for the example reservoirs were evaluated using the parameters determined from the linear relationship. The results demonstrated that the analytical decline analysis model is not only suitable for naturally-fractured reservoirs developed by water flooding but also for other types of water drive reservoirs. An analytical oil recovery model was also proposed. The results showed that the analytical model could match the oil production data satisfactorily. We also demonstrated that the frequently-used nonlinear type curves could be transformed to linear relationships in a log-log plot. This may facilitate the production decline analysis. Introduction Estimating reserves and predicting production in reservoirs has been a challenge for a long time. Many methods have been developed in the last several decades. One frequently-used technique is decline curve analysis approach. There have been a great number of papers on this subject1–23. Most of the existing decline curve analysis techniques are based on the empirical Arps equations4: exponential, hyperbolic, and harmonic equations. It is difficult to foresee which equation the reservoir will follow. On the other hand, each approach has some disadvantages. For example, the exponential decline curve tends to underestimate reserves and production rates; the harmonic decline curve has a trendency to overpredict the reservoir performance2. In some cases, production decline data do not follow any model but cross over the entire set of curves8. Fetkovich15 combined the transient rate and the pseudosteady-state decline curves in a single graph. He also related the empirical equations of Arps4 to the single-phase flow solutions and attempted to provide a theoretical basis for the Arps4 equations. This was realized by developing the connection between the material balance and the flow rate equations based on his previous papers24,25. Many derivations11,13 were based on the assumption of single-phase oil flow in closed boundary systems. These solutions were only suitable for undersaturated (single-phase) oil flow. However many oilfields are developed by water flooding. Therefore two-phase fluid flow instead of single-phase flow occurs. In this case, Lefkovits et al.19 derived the exponential decline form for gravity drainage reservoirs with a free surface by neglecting capillary pressure. Fetkovich et al.18 included gas-oil relative permeability effects on oil production for solution gas drive through pressure ratio term, This assumes that the oil relative permeability is a function of pressure. It is known that gas-oil relative permeability is a function of fluid saturation which dependents on fluid/rock properties. In water flooding, oil relative permeability can not be approximated as a function of pressure. The pressure during water flooding may increase, decrease, or remain unchanged. The oil production decline because of oil relative permeability reduction is associated with decrease in oil saturation instead of pressure in this case. Masoner21 correlated oil relative permeability to the Arps decline exponent by assuming a constant pressure potential and a pseudosingle-phase oil flow.